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what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n
Solution) limit n-->inf. [1 + (n!-n^n)/n^n]^1/n
= e^ limit n-->inf. {(n!-n^n)/n^n}.1/n
(applying formula lim x-->a [1 + f(x)]^g(x) = e ^ {lim x-->a f(x).g(x)} )
=e ^ lim n-->inf. (n-1)!/(n)^n-1 - 1/n
=e ^ lim n---> inf. (1-1/n)(1-2/n)(1-3/n)......1/n - 1/n
=e ^ (1-o)(1-0).....(1-0).0 - 0
=e ^ 0-0
=1
hence, integation 1= x + C
FIND PRODUCT (-41)*(102)
what does 4/100+1/10=
Example of Circles - Common Polar Coordinate Graphs Example: Graph r = 7, r = 4 cos θ, and r = -7 sin θ on similar axis system. Solution The very first one is a circle
cos inverse x -cos inverse 2x=pie\2
10p=100
Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.
2.5 in\ \/
in one point of the circle only one tangent can be drawn. prove
Show that the first-order integrated rate expression can be written as [A] t = [A] 0 e -n(in)t where n represents the number of elapsed halftimes. Sketch the plot of [A] 1
degree of a diffrential equation
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